JEE Main 201912 Apr, Evening shiftMathematicsHardMatrices and Determinants245× since 2002A value of θ∈(0,π3)\theta \in \left( {0,{\pi \over 3}} \right)θ∈(0,3π), for which ∣1+cos2θsin2θ4cos6θcos2θ1+sin2θ4cos6θcos2θsin2θ1+4cos6θ∣=0\left| {\matrix{ {1 + {{\cos }^2}\theta } & {{{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {1 + {{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {{{\sin }^2}\theta } & {1 + 4\cos 6\theta } \cr } } \right| = 01+cos2θcos2θcos2θsin2θ1+sin2θsin2θ4cos6θ4cos6θ1+4cos6θ=0, is :AOption A. π18{\pi \over {18}}18πBOption B. π9{\pi \over {9}}9πCOption C. 7π24{{7\pi } \over {24}}247πDOption D. 7π36{{7\pi } \over {36}}367πCheckSkip · show solution
